Question

Determine the centroid of the homogeneous plate, with respect to the given axes.
Also determine the moment of inertia in Ix

Y 10 cm 40 cm 20 cm 40 cm X 20 cm

Note:
* For the semicircle the centroidal moment of inertia at x is equal to
0.1098R ^ 4
*For the triangle, the centroidal moment of inertia at x is equal to
bh³ / 36

Answer 1

ny 40 20 90 > + AU dimensions are incm. go um 1 M (11 40 ♡ 20 n. 20. 20 20 given Homogeneous place is devided into 6 figures. Figure No centraid location wrd to given quil "Cuy) Area at given figure (cm²) (I) > 80 400 (20, 10/3) 800 (5) 100 80 3 400 3 (45 , 20 ) 400 (55, 10) 200 VE (90,- ) 200 TT

centraid of combined figure (ne. Ye.) Now "c= {Aini EAU (ewhere 2 - 1,11,11.,...,1) -) = 400 do + Bongo y|100*1907 400895 +501557.90 2001 400 +TUD 1900 +400+200 + 2001 Me= 28.38 Y- {Ażyi -) Yo ZAZ 100% go 48horagit 4001 80 + 4000 do +200 110 + 9001TYX-801 3 900 / 860 + 400+400+ 200 + 2001 30 =) Je = 12.92 = ) contraid = (Mg, telefon 11-90) (28.38, 12.82 Inate II Area will not be considered because it's absent. an calculation of centraid as well as moment af area.

Figure No magnitude (M4) Formula for anettioli contraid about anis 11 to n-anis and palsing through centroid 80) bh 20903 36 36 (90,2013) be 401409 36 36 I, I I 129 104 36. 11 1. 2560 104 36 I Im 10. TII (100, 80) (190,89 bh? 36 201403 36 128 1104 36 IT I (45,20) bal 3. 10 * 403 12 640 104. 12. I I I (55,10) ba3 12 = 108 209. 8x204. 12 12. + Før figure VI it mament of Inertia about vi- quis IT R4 8 TIX 204. 8 21 x 10 4 om (11.)n = 6.283 104 cm + (51), = 1; + A :(41) =)| (11) 320104 cmA 1287104 + 100 ml 36

2 200 199-) 36 • (TA)n = Illit A (1) 25671041300 140 |(19)n = 21.331104 cm (I'm In + I'm + Am (Y) 000 K (B9) IN UNIT 2 128 1104 tooox ti 3610 => ()n = 32 x 104 cm + Imlu - II + Apo (live) (Iv)n = 21.330100 TC MAN 64109 + 9001 (80) 2. 12 00 + 200 x 10 2 Non 12 (Ion I + Aly) 2 - 80104 (Iv)n = 2.62*104 In → moment at area at homogeneous figuure. - In = (Ithuy+ (1) + (Italy + (I vin + (1 127) u. Memo (32 +8%99+32 +29.33 +9.67 +6•2879104 TO 11.60.10 ama In = 94.28 cm x 104 In -)